The primary objective of this study is to test whether the administration of supplemental oxygen to infants who develop moderate retinopthy of prematurity (ROP) will result in a reduction of at least one third in the number of infants with eyes progressing to threshold ROP. Infants receive continuous pulse oximetry saturation monitoring at one of two specified oxygen levels with weekly measurement of ROP status. The Philadelphia STOP-ROP Clinical Center remains active at the Children's Hospital of Philadelphia (CHOP) as part of a consortium of four intensive care units. Eighteen (18) patients have been enrolled to date since recruitment began in 1994. Participation in this protocol will continue with enrollment of eligible patients. Opthalmologists will continue ROP screening exams in the nurseries and will alert study personnel of babies who are at risk for developing pre-threshold ROP.